- #1
Simkate
- 26
- 0
I just want to know if what i did is correct...please help Thank YOU!
∑(n =200 to ∞) ( -1)^n (1-1/n)^n = (-1 + 1/n)
This is a alternation Series
therefore the 2 condtions need to be satisfied for it to be Convergent.
i) is true
ii) lim b_n = 0 ?
L= lim (n--> ∞) (1-1/n)^n
= lim ( n--> 0^+) ln (1-t) / t = -1
= lim(n-->0^+) ln (-1/1/t) / (1) = -1
Thus, L=e^-1 = 1/e which not equal to O.
Therefore the series is not absolutely convergent and is divergent
AM I CORRECT?
∑(n =200 to ∞) ( -1)^n (1-1/n)^n = (-1 + 1/n)
This is a alternation Series
therefore the 2 condtions need to be satisfied for it to be Convergent.
i) is true
ii) lim b_n = 0 ?
L= lim (n--> ∞) (1-1/n)^n
= lim ( n--> 0^+) ln (1-t) / t = -1
= lim(n-->0^+) ln (-1/1/t) / (1) = -1
Thus, L=e^-1 = 1/e which not equal to O.
Therefore the series is not absolutely convergent and is divergent
AM I CORRECT?
Last edited: